8x^2-7x=7x^2+2

Solution for 8x^2-7x=7x^2+2 equation:

8x^2-7x=7x^2+2

We move all terms to the left:

8x^2-7x-(7x^2+2)=0

We get rid of parentheses

8x^2-7x^2-7x-2=0

We add all the numbers together, and all the variables

x^2-7x-2=0

a = 1; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·1·(-2)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{57}}{2*1}=\frac{7-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{57}}{2*1}=\frac{7+\sqrt{57}}{2}
$